Low-dimensional interacting electron systems in a magnetic field

We study the renormalization of a single impurity potential in one-dimensional interacting electron systems in the presence of magnetic field. Using the bosonization technique and Bethe ansatz solutions, we determine the renormalization group flow diagram for the amplitudes of scattering of up- and down-spin electrons by the impurity in a quantum wire at low electron density and in the Hubbard model at less than half filling. In the absence of magnetic field the repulsive interactions are known to enhance backscattering and make the impurity potential impenetrable in the low-energy limit. On the contrary, we show that in a strong magnetic field the interaction may suppress the backscattering of majority-spin electrons by the impurity potential in the vicinity of the weak-potential fixed point. This implies that in a certain temperature range the impurity becomes almost transparent for the majority-spin electrons while it is impenetrable for the minority-spin ones. The impurity potential can thus have a strong spin-filtering effect.We study the renormalization of a single impurity potential in one-dimensional interacting electron systems in the presence of magnetic field. Using the bosonization technique and Bethe ansatz solutions, we determine the renormalization group flow diagram for the amplitudes of scattering of up- and down-spin electrons by the impurity in a quantum wire at low electron density and in the Hubbard model at less than half filling. In the absence of magnetic field the repulsive interactions are known to enhance backscattering and make the impurity potential impenetrable in the low-energy limit. On the contrary, we show that in a strong magnetic field the interaction may suppress the backscattering of majority-spin electrons by the impurity potential in the vicinity of the weak-potential fixed point. This implies that in a certain temperature range the impurity becomes almost transparent for the majority-spin electrons while it is impenetrable for the minority-spin ones. The impurity potential can thus have a strong spin-filtering effect.

arXiv:cond-mat/0412403Physical Review BJul 1, 200521 citations

Interacting Electrons in Reduced Dimensions

D. Baeriswyl, David K Campbell

NATO ASI series. Series B : PhysicsJan 1, 198978 citations

Tunneling into a two-dimensional electron system in a strong magnetic field

Song He, P. M. Platzman, Bertrand I. Halperin

We investigate the properties of the one-electron Green's function in an interacting two-dimensional electron system in a strong magnetic field, which describes an electron tunneling into such a system. From finite-size diagonalization, we find that its spectral weight is suppressed near zero energy, reaches a maximum at an energy of about 0.2 ${\mathit{e}}^{2}$ /\ensuremath{\epsilon} ${\mathit{l}}_{\mathit{c}}$ , and decays exponentially at higher energies. We propose a theoretical model to account for the low-energy behavior. For the case of Coulomb interactions between the electrons, at even-denominator filling factors such as \ensuremath{\nu}=1/2, we predict that the spectral weight varies as ${\mathit{e}}_{0}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\omega}}}$/\ensuremath{\Vert}\ensuremath{\omega}\ensuremath{\Vert}, for \ensuremath{\omega}\ensuremath{\rightarrow}0.We investigate the properties of the one-electron Green's function in an interacting two-dimensional electron system in a strong magnetic field, which describes an electron tunneling into such a system. From finite-size diagonalization, we find that its spectral weight is suppressed near zero energy, reaches a maximum at an energy of about 0.2${\mathit{e}}^{2}$/\ensuremath{\epsilon}${\mathit{l}}_{\mathit{c}}$, and decays exponentially at higher energies. We propose a theoretical model to account for the low-energy behavior. For the case of Coulomb interactions between the electrons, at even-denominator filling factors such as \ensuremath{\nu}=1/2, we predict that the spectral weight varies as ${\mathit{e}}_{0}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\omega}}}$/\ensuremath{\Vert}\ensuremath{\omega}\ensuremath{\Vert}, for \ensuremath{\omega}\ensuremath{\rightarrow}0.

arXiv:cond-mat/9306020Physical Review LettersAug 2, 1993123 citations

One-dimensional bosonization approach to higher dimensions

Vladimir A. Zyuzin

This dissertation is devoted to theoretical studies of strongly interacting one-dimensional and quasi one-dimensional electron systems. The properties of one-dimensional electron systems can be studied within the bosonization technique, which presents fermions as collective bosonic density excitations. The power of this approach is the ability to treat electron-electron interaction exactly in the low-energy limit. The approach predicts the failure of Fermi liquid and an absence of long-range order in one-dimensions. The low-energy description of one-dimensional interacting systems is called the Tomonaga-Luttinger liquid theory. For example, the edges of quantum Hall systems are one-dimensional and described by a chiral Tomonaga-Luttinger liquid. Another example is a quantum spin Hall system with helical edge states, which are also described by a Tomonaga-Luttinger liquid. In our first work, a study of magnetized edge states of quantum spin-Hall system is presented. A magnetic field dependent signature of such edges is obtained, which can be verified in a Coulomb drag experiment. The second part of the dissertation is devoted to quasi-one dimensional antiferromagnetic lattices. A spatially anisotropic lattice antiferromagnet can be viewed as an array of one dimensional spin chains coupled in a way to match the lattice symmetry. This allows to use the non-Abelian bosonization technique to describe the low-energy physics of spin chains and study the inter-chain interactions perturbatively. The work presented in the dissertation studies the effect of Dzyaloshinskii-Moriya interaction on the magnetic phase diagram of the spatially anisotropic kagome antiferromagnet. We predict a Dzyaloshinskii-Moriya interaction driven phase transition from Neel to Neel+dimer state. In the third work, a novel model of the fractional quantum Hall effect is given. Wave functions of two-dimensional electrons in strong and quantizing magnetic field are essentially one-dimensional. That invites one to use the one-dimensional phenomenological bosonization to describe the density fluctuations of the two-dimensional interacting electrons in magnetic field. Remarkably, the constructed trial bosonized fermion operator describing the electron states with a fixed Landau gauge momentum is effectively two-dimensional.This dissertation is devoted to theoretical studies of strongly interacting one-dimensional and quasi one-dimensional electron systems. The properties of one-dimensional electron systems can be studied within the bosonization technique, which presents fermions as collective bosonic density excitations. The power of this approach is the ability to treat electron-electron interaction exactly in the low-energy limit. The approach predicts the failure of Fermi liquid and an absence of long-range order in one-dimensions. The low-energy description of one-dimensional interacting systems is called the Tomonaga-Luttinger liquid theory. For example, the edges of quantum Hall systems are one-dimensional and described by a chiral Tomonaga-Luttinger liquid. Another example is a quantum spin Hall system with helical edge states, which are also described by a Tomonaga-Luttinger liquid. In our first work, a study of magnetized edge states of quantum spin-Hall system is presented. A magnetic field dependent signature of such edges is obtained, which can be verified in a Coulomb drag experiment. The second part of the dissertation is devoted to quasi-one dimensional antiferromagnetic lattices. A spatially anisotropic lattice antiferromagnet can be viewed as an array of one dimensional spin chains coupled in a way to match the lattice symmetry. This allows to use the non-Abelian bosonization technique to describe the low-energy physics of spin chains and study the inter-chain interactions perturbatively. The work presented in the dissertation studies the effect of Dzyaloshinskii-Moriya interaction on the magnetic phase diagram of the spatially anisotropic kagome antiferromagnet. We predict a Dzyaloshinskii-Moriya interaction driven phase transition from Neel to Neel+dimer state. In the third work, a novel model of the fractional quantum Hall effect is given. Wave functions of two-dimensional electrons in strong and quantizing magnetic field are essentially one-dimensional. That invites one to use the one-dimensional phenomenological bosonization to describe the density fluctuations of the two-dimensional interacting electrons in magnetic field. Remarkably, the constructed trial bosonized fermion operator describing the electron states with a fixed Landau gauge momentum is effectively two-dimensional.

May 1, 20120 citations

Interacting electron gas in a strong magnetic field

P. Schlottmann, Rolf R. Gerhardts

The European Physical Journal BDec 1, 19799 citations

{\mathit{e}}^{2}

/\ensuremath{\epsilon}

{\mathit{l}}_{\mathit{c}}

, and decays exponentially at higher energies. We propose a theoretical model to account for the low-energy behavior. For the case of Coulomb interactions between the electrons, at even-denominator filling factors such as \ensuremath{\nu}=1/2, we predict that the spectral weight varies as ${\mathit{e}}_{0}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\omega}}}$/\ensuremath{\Vert}\ensuremath{\omega}\ensuremath{\Vert}, for \ensuremath{\omega}\ensuremath{\rightarrow}0.